Compare Expressions: Is 0.5x×1 Equal to 0.5x+0?

Algebraic Identities with Multiplicative Properties

Are the expressions the same or not?

$0.5x\times1$

$0.5x+0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find out if these expressions are equal. Ready?

00:10 Remember, multiplying any number by one keeps it the same.

00:16 And adding zero to any number doesn't change its value.

00:20 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Are the expressions the same or not?

$0.5x\times1$

$0.5x+0$

2

Step-by-step solution

To determine if the expressions $0.5x \times 1$ and $0.5x + 0$ are the same, we will simplify each using the basic properties of arithmetic:

Step 1: Simplifying $0.5x \times 1$
By using the multiplicative identity, we know that multiplying any number by 1 does not change its value. Thus:
$0.5x \times 1 = 0.5x$
Step 2: Simplifying $0.5x + 0$
By using the additive identity, we know that adding zero to any number does not change its value. Thus:
$0.5x + 0 = 0.5x$
Step 3: Comparing the simplified expressions
From the above steps, we have:
$0.5x \times 1 = 0.5x$ and
$0.5x + 0 = 0.5x$

Since both expressions simplify to $0.5x$ , we can conclude that the expressions are indeed the same.

Therefore, the solution to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Identity Properties: Multiplying by 1 and adding 0 don't change values
Technique: Simplify $0.5x \times 1 = 0.5x$ and $0.5x + 0 = 0.5x$
Check: Both expressions equal $0.5x$ , so they are equivalent ✓

Common Mistakes

Avoid these frequent errors

Thinking multiplication and addition create different results
Don't assume 0.5x × 1 and 0.5x + 0 are different because they use different operations = wrong conclusion! The operations themselves don't matter if they don't change the value. Always apply identity properties: × 1 keeps values unchanged, + 0 keeps values unchanged.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$\( 20x \)$

$2\times10x$

FAQ

Everything you need to know about this question

Why does multiplying by 1 not change the expression?

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The multiplicative identity property states that any number times 1 equals itself. So $0.5x \times 1 = 0.5x$ because multiplying by 1 never changes a value!

Why does adding 0 not change the expression?

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The additive identity property says that adding zero to any number gives you the original number. So $0.5x + 0 = 0.5x$ because zero added to anything leaves it unchanged!

Do I always need to simplify both expressions to compare them?

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Yes! Always simplify each expression completely first. Then you can easily see if they're equal. It's much clearer to compare $0.5x$ and $0.5x$ than the original complex forms.

What if the expressions had different variables or coefficients?

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The same identity properties still apply! For example, $3y \times 1 = 3y$ and $3y + 0 = 3y$ . The operations × 1 and + 0 always leave expressions unchanged.

Can I test this with actual numbers?

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Absolutely! Try $x = 2$ : both expressions become $0.5(2) = 1$ . Try any value - you'll always get the same result from both expressions!

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